Transfer-matrix description of heterostructures involving superconductors and ferromagnets

Based on the technique of quasiclassical Green’s functions, we construct a theoretical framework for describing heterostructures consisting of superconductors and/or spin-polarized materials. The necessary boundary conditions at the interfaces separating different metals are formulated in terms of hopping amplitudes in a t-matrix approximation. The theory is applicable for an interface with arbitrary transmission and exhibiting scattering with arbitrary spin dependence. Also, it can be used in describing both ballistic and diffusive systems. We establish the connection between the standard scattering-matrix approach and the existing boundary conditions, and demonstrate the advantages offered by the t-matrix description.